Finite Group Databasebeta

C22×C8×C22⋊D53 #28247922

order13568
isoclinismisoclinic class of Dic106
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C210

Aliases

direct productC22×C8×C22⋊D53

Splittings

FittingC24×C8×C53 ⋊ C2
SylowC53 ⋊ C22×C8×D4

Subgroups

subgroupG/H
centerC23×C8C2×D53
commutatorC2×C53C24×C8
FrattiniC2×C4C24×D53
FittingC24×C8×C53C2
socleC24×C53C22×C4
prime radicalC23×C22⋊D53C4
cosocleC2×C4×C53C25
hypercenterC24×C8D53
hypocenterC53C22×C8×D4
LCSG ▷ C2×C53 ▷ C53
UCSC1 ◁ C23×C8 ◁ C24×C8

3694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6784

Conjugacy classes & character table

3488 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 1033398);